Isn’t that a double tax? Taxed at buyback time, and taxed when shareholder cashes out and realizes their gain? Though I guess a small (10%??) tax could still make buyback tax + dividend long term gains is still less than normal income tax.

Everything's a "double tax", but people only care sometimes, for whatever reason.

Triple actually. Corporate profits tax, new hypothetical buyback tax, and then again as capital gains when the shareholder sells.

I pay taxes on my income, on my purchases, on my property and again on my property’s appreciation when I sell.

I'm not trying to be obtuse, I'm genuinely curious how this would work and what changes to tax law would need to be made.

Would you tax the entity buying the stock (in case always a company since it's a buyback; which I think would be the only example of taxing a stock purchase), or the entity selling the stock (either an individual or a company, which is already potentially taxed as capital gains)?

If the goal is to tax it similar to dividends you would tax the person selling the stock but it's already taxed as capital gains, either long term (0%/15%/20%) or short term (marginal bracket rate).

you just taxed the folks selling it at the same time.

does the company get a tax break if it buys its shares back at less than it sold them for?